Question

A 8.00-kg box is suspended from the end of a light vertical rope. A time-dependent force is applied to the upper end of the rope, and the box moves upward with a velocity magnitude that varies in time according to v(t)?

Answer 1

The given question is incomplete. The complete question is as follows.

A 8.00-kg box is suspended from the end of a light vertical rope. A time-dependent force is applied to the upper end of the rope, and the box moves upward with a velocity magnitude that varies in time according to v(t)=(2.00m/s2)t+(0.600m/s3)t2. What is the tension on the rope when the velocity is 15 m/s.

Explanation:

It is known that relation between acceleration and time is as follows.

           a = $\frac{dV}{dt}$

           a = $2 + 2 \times 0.6t$ ............ (1)

As it is given that velocity is 15 m/s.

             15 = $2t + 0.6t^{2}$

               t = 3.604 sec

Substitute the value of "t" in equation (1) as follows.

           a = $2 + 2 \times 0.6t$

           a = $2 + 2 \times 0.6 \times 3.604 sec$

              = 6.325 $m/s^{2}$

Now, we will calculate the tension as follows.

               T = mg + ma

                  = 8[9.81 + 6.325]

                  = 129.08 N

thus, we can conclude that tension on the rope is 129.08 N when the velocity is 15 m/s.